How do I give my drawers more detail?
If your drawers are separate objects in reality, there are no reason not to make separate meshes in 3D, especially if you want to make some close shots of the desk. Also, you need to keep quads as much as possible, meaning surfaces that have 4 vertices and not 5 or more. For example let's take one of your drawer:


Make it a separate mesh (I've deleted the rest of the object to make it simpler).
It looks like you have a lot of overlaying vertices, so to clean all this press W > Remove Doubles. On the top of the 3D view the amount of deleted vertices will be displayed.
Delete useless vertices with X > Dissolve Vertices.
Also delete vertices that are not part of any face with X > Delete Vertices.
To make quads, use the knife, K to activate, C to cut orthogonally.
Once you have only quads, extrude the whole surface with E.
If the normals are flipped, press ctrlN.
Now you have the facade of one drawer.
You can add depth with some edge loops ctrlR and extrudes E.
Etc...